But it’s sooo last century. 
If they’re feeling a bit nostalgic, I could see them changing names to:
Disney Searchlight
Disney Century
They certainly would want to avoid any connection with Fox, when there will be a separate media company called Fox going forward.
I’m betting Fox Searchlight Pictures will simply become “Searchlight Pictures”. Would be cool to keep the same logo and everything.
Blue Sky will elevated to the same level as Pixar and will run as a separate animation studio. The resources of Fox Animation (parent of Blue Sky) will probably be rolled into both Walt Disney Animation Studios and Blue Sky.
20th Century Disney Pictures? 
21st Century Disney. 
If they intend to remove the Fox name, this would be the most logical way.
(For those who don’t know 20CF was a result of a merge between 20th Century Pictures and Fox Films back in Ye olde times)
Love the idea of just taking it back to 20th Century Pictures.
No doubt Disney acquires fox for the content but it would be a shame to just fold their whole legacy. Disney no longer have a studio that releases more adult oriented features (Touchstone yes but isn’t really used these days) 20th Century Features can be just that, a studio subsidiary of Disney that focuses more so on adult content than the family friendly viewing material Disney make. Don’t get me wrong, I love Disney but there needs to be a place for more adult skewing content.
Greg Meidel, president of Twentieth Television (Fox’s TV sales and syndication division) and MyNetworkTV, has left the company as the result of the Disney-Fox merger. Under the merger deal, MyNetworkTV will remain part of the new Fox Corporation.
What about 30th Century Fox?
Sure. In about 900 years. 
Question would be, what rights does Disney maintain to the Fox name post-sale and merger?
Can they use the name indefinitely or do they have to remove Fox references within a few years?
Good question. Maybe it’s similar to Warner Music and Universal Music who can use the names of their former parent companies indefinitely?
There’s a “30th Century” one shown at the end of Futurama
As a piss take.
I can’t seem to find the source I read a couple of days ago, but apparently Disney are licensing the “Fox” part of the name in their new acquisitions from Fox Corp.
It probably won’t be a longtime concern, considering likely rebrands to drop the “Fox” part and dissolution/redistribution of others.
Almost certainly, yes.
The Disney-Fox merger is now affecting both companies’ operations in Australia, with three senior executives leaving.
From article:
It is unclear how many [20C Fox Sydney] will segue to Disney’s Melbourne office but most may be unwilling to make that move even if they are offered jobs
Fact? Assumption? These sort of things happen a lot (relocations), surely if incentives are offered ($$$$$$$) 
So is Disney’s Australian office based in Melbourne?
I just googled it. They’re based in Richmond.
I thought they were in South Yarra, within the ‘Jam Factory’? Close to Village Roadshow’s global HQ as well
